On Symbolic Solutions of Algebraic Partial Differential Equations

被引：0

作者：

Grasegger, Georg ^{[1
,2
]}

Lastra, Alberto ^{[3
]}

Sendra, J. Rafael ^{[3
]}

Winkler, Franz ^{[2
]}

机构：

[1] Johannes Kepler Univ Linz, Doctoral Program Computat Math, A-4040 Linz, Austria

[2] Johannes Kepler Univ Linz, Symbol Computat Res Inst, A-4040 Linz, Austria

[3] Univ Alcala de Henares, Dpto Fis Matemat, E-28871 Alcala De Henares, Spain

来源：

COMPUTER ALGEBRA IN SCIENTIFIC COMPUTING, CASC 2014 | 2014年 / 8660卷

基金：

奥地利科学基金会;

关键词：

Partial differential equations; algebraic surfaces; rational parametrizations; radical parametrizations; RATIONAL GENERAL-SOLUTIONS; PARAMETRIZATION;

D O I：

暂无

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper we present a general procedure for solving first-order autonomous algebraic partial differential equations in two independent variables. The method uses proper rational parametrizations of algebraic surfaces and generalizes a similar procedure for first-order autonomous ordinary differential equations. We will demonstrate in examples that, depending on certain steps in the procedure, rational, radical or even non-algebraic solutions can be found. Solutions computed by the procedure will depend on two arbitrary independent constants.

引用

页码：111 / 120

页数：10

共 50 条

[1] Symbolic solutions for a class of partial differential equations
DeJager, B
VanAsch, B
[J]. JOURNAL OF SYMBOLIC COMPUTATION, 1996, 22 (04) : 459 - 468
[2] ON SOLUTIONS WITH ALGEBRAIC CHARACTER OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS
BERGMAN, S
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1950, 68 (MAY) : 461 - 507
[3] Analytical solutions for systems of partial differential-algebraic equations
Benhammouda, Brahim
Vazquez-Leal, Hector
[J]. SPRINGERPLUS, 2014, 3 : 1 - 9
[4] ALGEBRAIC SOLUTIONS OF ALGEBRAIC DIFFERENTIAL EQUATIONS
Gao LingyunDept. of Math.
[J]. Applied Mathematics:A Journal of Chinese Universities, 2005, (01) : 45 - 50
[5] Algebraic solutions of algebraic differential equations
Gao L.
[J]. Applied Mathematics-A Journal of Chinese Universities, 2005, 20 (1) : 45 - 50
[6] Symbolic methods to construct exact solutions of nonlinear partial differential equations
Hereman, W
Nuseir, A
[J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 1997, 43 (01) : 13 - 27
[7] Expressions of Solutions of Linear Partial Differential Equations Using Algebraic Operators and Algebraic Convolution
Bikulciene, Liepa
Navickas, Zenonas
[J]. NUMERICAL ANALYSIS AND ITS APPLICATIONS: 4TH INTERNATIONAL CONFERENCE, NAA 2008, 2009, 5434 : 208 - +
[8] Algebraic Differential Equations - Parametrization and Symbolic Solution
Winkler, Franz
[J]. ALGEBRAIC INFORMATICS, CAI 2019, 2019, 11545 : XIII - XIV
[9] On the solutions of algebraic differential equations
Mahler, K
[J]. PROCEEDINGS OF THE KONINKLIJKE NEDERLANDSE AKADEMIE VAN WETENSCHAPPEN, 1939, 42 (1/5): : 61 - 63
[10] LIE ALGEBRAIC METHODS AND SOLUTIONS OF LINEAR PARTIAL-DIFFERENTIAL EQUATIONS
DATTOLI, G
RICHETTA, M
SCHETTINI, G
TORRE, A
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 1990, 31 (12) : 2856 - 2863

← 1 2 3 4 5 →